一种结构动力响应分析的快速高阶算法

为了提高基于高阶格式的结构动力响应微分求积分析方法的计算效率，发展了一种求解动力方程的快速算法．利用微分求积原理将结构动力方程转化为标准Sylvester方程的形式，通过对系数矩阵进行矩阵分解，进而将动力响应Sylvester方程化为一系列标准线性方程组，采用相关成熟算法求解这些线性方程组后即可获得结构动力时程响应的全部解答．结构动力响应微分求积分析方法为高阶数值方法，一步计算可以获得多个时点处的动力响应．基于本文快速算法，不必直接对矩阵方程进行求解．数值算例表明，本文快速算法能够准确地计算出结构动力响应，具有数值精度高、收敛性好的优点．

A Fast Algorithm for High-Order Dynamic Response Analysis of Structures

A fast algorithm is proposed for the solution of the equation of motion in this paper, in order to improve the computational efficiency of the differential quadrature-based dynamic procedure of structures. The differential equation governing the forced dynamic vibration of the system is converted into the standard Sylvester equation by employing the differential quadrature rule. Then, the linear algebraic equations are obtained via decomposition of the coefficient matrice of the Sylvester equation. Thus, all the dynamic responses of the system can be obtained by solving these linear algebraic equations one by one with the effective numerical methods. The differential quadrature-based dynamic procedure is a high-order dynamic approach in which the dynamic responses over a time interval consisting of several time steps can be calculated simultaneously. Therefore, it is unnecessary to solve the matrix equation that governs the dynamic responses of the system. The numerical example shows that the proposed fast algorithm can obtain the accurate solution of the dynamic response, with high precision and good convergence.